Question

Find the center and radius of the circle whose equation is given below: (x − 2.5)2 + (y + 5.4)2 = 1.21

Answer 1

The center of the circle is (2.5, 5.4) and the radius of the circle is 1.1

Explanation:

We are to find the center and radius of the circle whose equation is given as;

(x − 2.5)² + (y + 5.4)² = 1.21 ----------------------------------------------------(1)

All we need to do is to compare it with a standard equation of a circle.

A standard equation of a circle with center (a,b) and radius r is given as;

(x -a)² + (y - b)² = r² ---------------------------------------------------------(2)

where a, b is the center of the circle and r is the radius of the circle

Comparing equation (1) and (2)

C(2.5 , 5.4)

r² = 1.21

But what we are looking for is just r, so we will take the square root of both-side

√r² = √1.21

r= 1.1

Therefore the center of the circle is (2.5, 5.4) and the radius of the circle is 1.1

Answer 2

The center is at (2.5, -5.4) and the radius is 1.1

Explanation:

The formula for a circle is

(x-h)^2 + (y-k)^2 = r^2

Where (x,k) is the center and r is the radius)

(x − 2.5)^2 + (y + 5.4)^2 = 1.21

(x − 2.5)^2 + (y - - 5.4)^2 = 1.1^2

The center is at (2.5, -5.4) and the radius is 1.1